In introductory mechanics, the momentum of a particle is its mass times its velocity. In electrodynamics, the momentum of a field is proportional to the cross-product of the electric field with the magnetic field. In special relativity, momentum is generalized to four-momentum.

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Operator algebra for momentum and magnetic vector potential

Let $\vec{A}$ be the magnetic vector potential and $\vec{p}$ be momentum. $$ \vec{p} \cdot \vec{A} \psi = (\vec{p} \cdot \vec{A}) \psi + \vec{A} \cdot (\vec{p} \psi) $$ $$ \vec{A} \cdot \vec{p} \psi =...
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47 views

How impulse relates to momentum? is this correct?

Knowing that: $$F=\frac{dp}{dt}$$ I manipulate the equation a bit to say: $$Fdt=dp$$ Then ingrate both sides... $$\int{F}dt = p$$ From what I've read, isn't the change in momentum related to the ...
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2answers
126 views

What happens when two bodies collide in a dynamics point of view?

I'm a high school student learning about energy and momentum. What confuses me is the things with elastic and inelastic collisions. I completely (in my opinion) understand those concepts in energy ...
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1answer
35 views

How do i find how long an object can coast for?

I am given the mass of an object (a motorcycle), its velocity, the mass of its wheels, and the radius of the wheels. If the object rolls without slipping, how can I possibly find out how high it can ...
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2answers
61 views

Momentum Equation VS Momentum of Momentum Equation

Newton's second law states that the linear momentum ($P$) rate is equal to the net force: $$F=\frac{d}{dt}P \tag{1} $$ On the other side, there is a same expression for angular momentum ($L$): $$M=\...
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144 views

Conservation of mechanical energy isn't giving me the right answer? [closed]

I have been trying to solve this question: You are working for a shipping company. Your job is to stand at the bottom of an 8.0 m long ramp that is inclined at 37 degrees above the horizontal. You ...
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1answer
74 views

Do particles also have intrinsic linear momentum (linear analogue of spin)?

We know from quantum mechanics that microscopic particles have spin, which is a kind of intrinsic angular momentum. The particle has angular momentum without physically rotating. In a similar way, do ...
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1answer
53 views

Law of conservation of momentum , elastic collision [closed]

In Law of Conservation of momentum , elastic collision occurs only in an isolated system. A case defined as,when Object A comes with initial velocity and collides with object B which is in rest V= ...
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1answer
34 views

Rigid Balls aligned along a line in vacuum

Recently I've been trying to visualize a situation where i have these really rigid identical balls aligned along a line so close to each other in vacuum.Now if I were to apply an impulsive force to ...
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2answers
176 views

Is the reaction force for a stone hitting a wall infinite?

Let us assume a rigid stone which moves in empty space with a constant speed of $v$. (Or in the air with no friction and drag or you can imagine a free fall with friction). This stone hits a rigid ...
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0answers
17 views

Motion in Spaces [duplicate]

How does a shuttle move in the space as, the whole mechanism of a rocket is based on 3rd law of newton but, we can not apply 3rd law of newton in space because there is no reactive force in space?
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2answers
83 views

Conflicts between Bernoulli's Equation and Momentum Conservation?

The well known Bernoulli's equation states that $P+\frac{\rho V^2}{2}=c$ However, a simple momentum conservation considering $P_1$ and $P_2$ acting on two sides, and velocity changes from $V_1$ to $...
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3answers
170 views

Derivation of momentum operator

From a video lecture on quantum mechanics at MIT OCW I found that you didn't need to know Schrödinger's equation to know the momentum operator which is $\frac{\hbar}{i}\frac{\partial}{\partial x}$. ...
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2answers
112 views

How can photons cause charges to attract? [duplicate]

Photons are the force carrier of the electromagnetic force. I do not see how this could result in a transfer of momentum that attracts objects together. I am primarily interested in an intuitive ...
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1answer
96 views

When are energy, mechanical energy, momentum, and angular momentum conserved?

I am in AP Physics and my only real hangup is knowing when the said quantities are conserved. Please define what is the SYSTEM in your answer. I kind of have the basic idea. For example, if there ...
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0answers
23 views

How is conservation of momentum preserved in antimatter annihilation? [duplicate]

If an anti-proton collides with a proton, they are supposed to totally annihilate each other, correct? Then how is conservation of momentum preserved? Could you launch both protons and antiprotons ...
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0answers
40 views

Will the flash light accelerate in space? [duplicate]

As we know from school physics course light has pressure. So my question is will flash light accelerate in space in the direction opposite to light emission? If not, then will flash light with ...
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2answers
70 views

Which has the larger change in momentum [closed]

This is a concept question in my physics class, It isn't for marks, its just to gauge your understanding of the subject. I'm not sure if I have the right idea. since the mass of block A is 4 times ...
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0answers
42 views

Relativistic momentum (Lorentz boost) low velocity expansion

If I have a momenta $p^{\mu}=(E, p_x, p_y, p_z)$ and transform it via lorentz boost in x-direction with velocity v I'll get for the new 0th component $E'=\gamma E + \gamma v p_x$ why is this in the ...
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1answer
53 views

Simple frame of reference problem (conservation of momentum?)

I'm having trouble wrapping my head around a particular concept. Suppose we have a machine that fires balls of speed $u$ at some mass rate $\sigma$ (of units $\frac{kg}{s}$) directly at a car of mass $...
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1answer
69 views

Momentum operator derivation in QFT from QM

In David Tong`s QFT notes there is a chapter about the derivation of the momentum operator from quantum mechanics (page 44) where he is showing that the momentum operator can be expressed by the ...
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1answer
39 views

Conservation of momentum in inelastic conservation

Why does momentum and velocity change along contact normal but not contact tangent In in elastic collision? Suppose a ball strike an inelastic surface. It's velocity component does not change along ...
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1answer
8 views

Calculating the force $F$ for wich $S_2$ will be in uniform motion

The sketch is given: The double pulley groove of radius $r=5\;\mathrm{cm}$ and $R=10\;\mathrm{cm}$ is in rotation Two inextensible wires of negligible masses are wound around each ...
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2answers
81 views

Does a conservation of momentum problem need to specify velocity, not just speed?

Problem: A $100$ g bullet is fired from a $10$ kg gun with a speed of $1000$ m/s. What is the speed of the recoil of the gun? This problem can be solved, if it can, using the law of conservation of ...
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3answers
171 views

Derivation of $E=pc$ for a massless particle?

In classical mechanics, massless particles don't exist because for $m=0$, $p=0$. The relativistic relation between energy, mass and spatial momentum is: $E^2= (pc)^2 + (mc^2)^2$ . So it is said that ...
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1answer
76 views

Does third law of motion apply to light or EM waves? [duplicate]

Third law of motion - "For every action there is an equal and opposite reaction" I was considering the situation, where I may be motionless in space with only a flashlight and no forces acting on me. ...
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1answer
253 views

Expectation value of momentum in any bound state [duplicate]

How do we prove that the expectation value of momentum operator in any bound state is zero ? $$ \langle \hat{P} \rangle_{\text{bound state}}=0 $$ and what about the position expectation value ? How ...
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5answers
207 views

What is the definition of linear momentum?

Every where and book I search I get that the definition of linear momentum is the amount of speed (quantity of motion) contained in it or simply it is mass $\times$velocity? So, what is an ...
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1answer
23 views

For elastic collisions, can I transfer mass to velocity?

I think my teacher said that because the momentum is the same if you multiply/divide mass and velocity by the same factor, you can make the masses equal and then do a shortcut. Is this right?
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1answer
73 views

Conservation of momentum homework problem [closed]

A 2-stage rocket travels $1200 \text{ m/s}$ relative to earth. When the first stage runs out of fuel, the explosive bolt separates the first stage from the second with a velocity of $35 \text{ m/s}$ ...
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1answer
31 views

Impulse and Momentum

Case 1- We have two masses of equal size. Mass 1, with positive velocity, collides with Mass 2. This causes Mass 1 to have 0 velocity in the end and Mass 2 to have a velocity. Case 2- A mass (1) ...
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171 views

Relation between $\Delta E$ and $\Delta p$

This will be a very quick question. I've seen in some books, that when describing the Heisenberg uncertainty principle, it was used implicitly the application of the following statement: $$\Delta E=\...
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2answers
161 views

Particle anti-particle annihilation and photon production

This is just a conceptual question I guess. The annihilation of a particle with a finite mass and its anti-particle cannot lead to the emission of only one photon, and this is due to the conservation ...
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2answers
113 views

The acceleration of the centre of mass [closed]

Given two balls that are thrown straight up in the air at a speed of $40 \:\mathrm{m/s}$, $0.10 \:\mathrm{s}$ apart. One ball is twice the mass of the other. The heavier ball is thrown second. I'm ...
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0answers
129 views

Why does gravity conserve linear momentum but not forces at a pivot point?

What forces count as an external force in the conservation of linear momentum? Consider an initially stationary rod that can rotate about one end-point. A ball comes in at a constant speed and ...
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3answers
156 views

Force of an object “skidding”?

Let's say I put the brakes on really suddenly in a car that was moving at 40mph. If I know how much force it takes to break the adhesion of the wheels, how do I find the force the car is exerting? ...
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31 views

The momentum representation of $x$ and $ [x,p]$ [duplicate]

To deduce the momentum representation of $[x,p]$, we can see one paradom $$<p|[x,p]|p>=iℏ$$ $$<p|[x,p]|p>=<p|xp|p>−<p|px|p>=p<p|x|p>−p<p|x|p>=0$$ Why? If we ...
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1answer
124 views

Conservation of energy or conservation of momentum- which one is applicable in this problem?

There was this question from Kleppner and Kolenkow's Classical Mechanics: PROBLEM: And I found its solution from this Link: It is quite an extended solution and I am not drawing you into the ...
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1answer
383 views

What is the initial velocity of an object, given a change in mass, and an exerted force [closed]

An 8.0-g bullet is shot into a 4.0-kg block, at rest on a frictionless horizontal surface (see the figure). The bullet remains lodged in the block. The block moves into an ideal massless spring and ...
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2answers
173 views

What happens to the kinetic energy of a system in a non-elastic collision? [duplicate]

I know that the kinetic energy of a system is NOT conserved in a non-elastic collision. But energy is supposed to be conserved, so where does all that energy go? Is it transformed into other forms ...
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1answer
121 views

Switch from the position representation to the momentum representation

If we use Fourier Transform, we can switch from the position representation to the momentum representation, like the following formula here comes the problem, if we use dirac notation we can see it ...
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1answer
36 views

Statics of a rigid solid [closed]

I need help with this problem... I need to calculate the angle so that this whole thing is in equilibrium. I don't have any problem with the conservation of the force. But when I get to the ...
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Why does the angular average of the divergence result in a factor 1/3?

In going from eq.(6.13) to (6.14) in http://www.nano.northwestern.edu/intranet/pubdocs/quasiclassical.pdf it is assumed that $$\displaystyle\int\dfrac{d\Omega_{\vec{p}}}{4\pi}\,(\hat{p}\cdot\hat{p})\...
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0answers
89 views

What is the effective electron mass in a plasma?

Is there a way to calculate the effective electron mass in plasmas? Effective electron mass is usually defined as varying from the vacuum electron mass in solid state physics. However, momentum ...
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1answer
199 views

Why is only angular momentum conserved for a planet and not linear momentum?

Suppose a planet is moving in an elliptical orbit with the Sun at one of its focii. I know that the forces in existence will be gravity which provides the necessary centripetal force. Now my book ...
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1answer
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Understanding elastic collisions of objects with the same velocities

I am having trouble understanding the following statement from my book: The law of cosines tells us that if the sides of a triangle obey the Pythagorean formula, they must form a right triangle. ...
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1answer
112 views

Questions about the velocity of the center of gravity

I have a physics test coming up in a couple of days and I really need to have some things explained to me. It is about something that I think is called in english "the velocity of the center of ...
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Why is the angular average of the direction of the momentum squared a third instead of one?

In the article http://www.nano.northwestern.edu/intranet/pubdocs/quasiclassical.pdf (in going from eq. (6.13) to eq. (6.14)) it is stated that $$\langle\hat{p}\cdot\hat{p}\rangle_{\hat{p}}=\dfrac{1}{3}...
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1answer
79 views

Why can we model a body to have a center of mass?

I accept that bodies have a center of mass. I also accept that if I were to suspend a body by only supporting it at its center of mass, then the body wouldn't rotate. In the scenario that we suspend a ...
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1answer
139 views

4-Momentum conservation for particle annihilation

Disclaimer: this is a homework question, so I am happy with just a hint or the expressions needed to proceed with my understanding. I am working on the momentum conservation of a particle/anti-...